Code:

import sympy

x = sympy.symbols('x')
equation = sympy.Eq(1/(x+4) - 1/(x-7), sympy.Rational(11, 30))

# Step 1: Combine fractions on the LHS
lhs_combined = sympy.simplify(1/(x+4) - 1/(x-7))
print(f"LHS combined: {lhs_combined}")

# Step 2: Set up the simplified equation
simplified_eq = sympy.Eq(lhs_combined, sympy.Rational(11, 30))
print(f"Simplified equation: {simplified_eq}")

# Step 3: Solve for x
solutions = sympy.solve(equation, x)
print(f"Solutions: {solutions}")

Output:

LHS combined: -11/((x - 7)*(x + 4))
Simplified equation: Eq(-11/((x - 7)*(x + 4)), 11/30)
Solutions: [1, 2]